The Banker's discount on a bill due 6 months hence at 16% per annum is Rs. 216. The true discount is :

Options

A. Rs. 212
B. Rs. 180
C. Rs 210
D. Rs. 200

Answer

To find the true discount given the banker's discount, we can use the formula:

\[ \text{True Discount} = \frac{\text{Banker's Discount} \times 100}{100 + \text{Rate} \times \text{Time}} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Banker's Discount (BD) = Rs. 216
- Rate (R) = 16% per annum
- Time (T) = 6 months = 0.5 years (since 6 months is half a year)

**Hint:** Convert months into years for the calculation.

2. **Calculate the effective rate for the time period:**
- The effective rate for 6 months at 16% per annum is:
\[ \text{Effective Rate} = R \times T = 16\% \times 0.5 = 8\% \]

**Hint:** Remember to convert the percentage into a decimal when performing calculations.

3. **Substitute the values into the formula:**
\[ \text{True Discount} = \frac{216 \times 100}{100 + 8} \]

**Hint:** Ensure you add the effective rate correctly to 100.

4. **Calculate the denominator:**
\[ 100 + 8 = 108 \]

**Hint:** Double-check your addition to avoid simple errors.

5. **Calculate the True Discount:**
\[ \text{True Discount} = \frac{21600}{108} \]

**Hint:** You can simplify the division by breaking it down or using a calculator.

6. **Perform the division:**
\[ \text{True Discount} = 200 \]

**Hint:** Make sure your division is accurate to ensure the final answer is correct.

### Final Answer:
The true discount is Rs. 200.